Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
386 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #23757615 | C2 | semidirect |
| 4. #23757615 | C2 | semidirect |
| 5. #23757609 | C2 | semidirect |
| 6. #23757604 | C2 | semidirect |
| 7. #23757315 | C2 | semidirect |
| 8. #23757311 | C2 | semidirect |
| 9. #23757283 | C2 | semidirect |
| 10. C2×#19097696 | C2 | semidirect |
| 126. C157 | #3097 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757844 | 2 |
| #23757756 | 2 |
| #23757615 | 2 |
| #23757609 | 2 |
| #23757604 | 2 |
| #23757315 | 2 |
| #23757311 | 2 |
| #23757283 | 2 |
| C2×#19097696 | 2 |
| #408×C157 | 2 |
| #3097 | 157 |